Abstract
Let Γ i , i = 0, 1, be two groups containing C p , the cyclic group of prime order p, as a subgroup of index 2. Let Γ = Γ0 * Cp Γ1. We show that the Nil-groups appearing in Waldhausen’s splitting theorem for computing K j (ℤΓ) (j≤ 1) vanish. Thus, in low degrees, the K-theory of ℤΓ can be computed by a Mayer-Vietoris type exact sequence involving the K-theory of the integral group rings of the groups Γ0, Γ1 and C p .
1 Supported in part by the SNF (Denmark) under grant number 9502188.
2 Supported in part by a Vanderbilt University Summer Research Fellowship.
3 Supported in part by National Science Foundation Grant DMS-9504479.
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Munkholm, H.J., Prassidis, S. (2001). On the vanishing of certain K-theory Nil-groups. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_19
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DOI: https://doi.org/10.1007/978-3-0348-8312-2_19
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